Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C4×C313 ⋊ C2 |
| Sylow | C313 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=e,c^2=e,b^a=bd,f^b=f^312,f^c=f^3121580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34094232, #34094234, #34094237, … |
| maximal normal subgroup of | #34094232, #34094234, #34094237, … |
| maximal quotient of | #34093999, C4⋊C4×Dic313, #34094023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 108);